Pušica started to play basketball in his hometown Belgrade, for the Partizan youth selections.

In 2013, Pušica was recruited to attend a prep school in Kansas, U.S., Sunrise Christian Academy in Bel Aire, a suburb of Wichita.

On August 18, Pušica signed with BC Labas GAS Prienai of the Lithuanian Basketball League.

On February 25, 2022, Pušica signed with Galatasaray Nef of the Basketbol Süper Ligi and Basketball Champions League.

[9] On November 16, 2022, he signed with Twarde Pierniki Toruń of the Polish Basketball League (PLK).

[12] Pušica was a member of the Serbian under-16 team that played at the 2011 FIBA Europe Under-16 Championship in the Czech Republic.